Basic properties
| Modulus: | \(8005\) | |
| Conductor: | \(8005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(400\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8005.cr
\(\chi_{8005}(2,\cdot)\) \(\chi_{8005}(8,\cdot)\) \(\chi_{8005}(58,\cdot)\) \(\chi_{8005}(62,\cdot)\) \(\chi_{8005}(128,\cdot)\) \(\chi_{8005}(187,\cdot)\) \(\chi_{8005}(232,\cdot)\) \(\chi_{8005}(308,\cdot)\) \(\chi_{8005}(438,\cdot)\) \(\chi_{8005}(488,\cdot)\) \(\chi_{8005}(512,\cdot)\) \(\chi_{8005}(573,\cdot)\) \(\chi_{8005}(673,\cdot)\) \(\chi_{8005}(717,\cdot)\) \(\chi_{8005}(722,\cdot)\) \(\chi_{8005}(928,\cdot)\) \(\chi_{8005}(992,\cdot)\) \(\chi_{8005}(1028,\cdot)\) \(\chi_{8005}(1113,\cdot)\) \(\chi_{8005}(1163,\cdot)\) \(\chi_{8005}(1232,\cdot)\) \(\chi_{8005}(1237,\cdot)\) \(\chi_{8005}(1293,\cdot)\) \(\chi_{8005}(1397,\cdot)\) \(\chi_{8005}(1473,\cdot)\) \(\chi_{8005}(1517,\cdot)\) \(\chi_{8005}(1543,\cdot)\) \(\chi_{8005}(1593,\cdot)\) \(\chi_{8005}(1682,\cdot)\) \(\chi_{8005}(1707,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{400})$ |
| Fixed field: | Number field defined by a degree 400 polynomial (not computed) |
Values on generators
\((1602,4806)\) → \((-i,e\left(\frac{39}{400}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) |
| \( \chi_{ 8005 }(8, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{50}\right)\) | \(e\left(\frac{139}{400}\right)\) | \(e\left(\frac{16}{25}\right)\) | \(e\left(\frac{67}{400}\right)\) | \(e\left(\frac{393}{400}\right)\) | \(e\left(\frac{23}{50}\right)\) | \(e\left(\frac{139}{200}\right)\) | \(e\left(\frac{287}{400}\right)\) | \(e\left(\frac{79}{80}\right)\) | \(e\left(\frac{3}{16}\right)\) |